{
  "id": "2210.09939",
  "version": "v1",
  "published": "2022-10-18T15:42:39.000Z",
  "updated": "2022-10-18T15:42:39.000Z",
  "title": "A variant of Wilson's functional equation on semigroups",
  "authors": [
    "Youssef Aserrar",
    "Abdellatif Chahbi",
    "Elhoucien Elqorachi"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We determine the complex-valued solutions of the following functional equation \\[f(xy)+\\mu (y)f(\\sigma (y)x) = 2f(x)g(y),\\quad x,y\\in S,\\] where $S$ is a semigroup and $\\sigma$ an automorphism, $\\mu :S\\rightarrow \\mathbb{C}$ is a multiplicative function such that $\\mu (x\\sigma (x))=1$ for all $x\\in S$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-18T15:42:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39B32",
      "39B52"
    ],
    "keywords": [
      "wilsons functional equation",
      "complex-valued solutions",
      "automorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}